Variance reduction for Markov chains with application to MCMC
نویسندگان
چکیده
منابع مشابه
Variance Reduction via Antithetic Markov Chains
We present a Monte Carlo integration method, antithetic Markov chain sampling (AMCS), that incorporates local Markov transitions in an underlying importance sampler. Like sequential Monte Carlo sampling, the proposed method uses a sequence of Markov transitions to guide the sampling toward influential regions of the integrand (modes). However, AMCS differs in the type of transitions that may be...
متن کاملGeometric Variance Reduction in Markov Chains. Application to Value Function and Gradient Estimation
We study a variance reduction technique for Monte Carlo estimation of functionals in Markov chains. The method is based on designing sequential control variates using successive approximations of the function of interest V . Regular Monte Carlo estimates have a variance of O(1/N), where N is the number of sample trajectories of the Markov chain. Here, we obtain a geometric variance reduction O(...
متن کاملVariance Bounding Markov Chains
We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all L functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Pesk...
متن کاملStability of Adversarial Markov Chains, with an Application to Adaptive MCMC Algorithms
We consider whether ergodic Markov chains with bounded step size remain bounded in probability when their transitions are modified by an adversary on a bounded subset. We provide counterexamples to show that the answer is no in general, and prove theorems to show that the answer is yes under various additional assumptions. We then use our results to prove convergence of various adaptive Markov ...
متن کاملThe ODE method for stability of skip-free Markov chains with applications to MCMC
Fluid limit techniques have become a central tool to analyze queueing networks over the last decade, with applications to performance analysis, simulation and optimization. In this paper, some of these techniques are extended to a general class of skip-free Markov chains. As in the case of queueing models, a fluid approximation is obtained by scaling time, space and the initial condition by a l...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Statistics and Computing
سال: 2020
ISSN: 0960-3174,1573-1375
DOI: 10.1007/s11222-020-09931-z